A k-space method for nonlinear wave propagation.

Abstract

A k-space method for nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation and is solved by a wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and 2-D problems are investigated to verify the method by comparing results to the finite element method. It is found that, in order to obtain accurate results in homogeneous media (errors of the fundamental and first two harmonics being less than 0.5 dB), the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant–Friedrichs–Lewy number can be as small as 0.4. As a result, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient than the conventional finite element method or finite-difference time-domain method for the conditions studied here. However, although the present method is highly accurate for weakly inhomogeneous media, it is found to be less accurate for strongly inhomogeneous media.